Managerial Finance l
Microsoft Word - Document1 Assignment 04 – Time, Value of Money, Part 2 BU340 – Managerial Finance l Directions: Unless otherwise stated, answer in complete sentences, and be sure to use correct English spelling and grammar. Sources must be cited in APA format. Your response should be four (4) pages in length; Respond to the items below. Part A Given the following cash inflow at the end of each year, what is the future value of this cash flow at 6%, 9%, and 15% interest rates at the end of the seventh year? Year 1 $15,000 Year 2 $20,000 Year 3 $30,000 Years 4 through 6 $0 Year 7 $150,000 Part B County Ranch Insurance Company wants to offer a guaranteed annuity in units of $500, payable at the end of each year for 25 years. The company has a strong investment record and can consistently earn 7% on its investments after taxes. If the company wants to make 1% on this contract, what price should it set on it? Use 6% as the discount rate. Assume that it is an ordinary annuity and the price is the same as present value. Part C A local government is about to run a lottery but does not want to be involved in the payoff if a winner picks an annuity payoff. The government contracts with a trust to pay the lump-sum payout to the trust and have the trust (probably a local bank) pay the annual payments. The first winner of the lottery chooses the annuity and will receive $150,000 a year for the next 25 years. The local government will give the trust $2,000,000 to pay for this annuity. What investment rate must the trust earn to break even on this arrangement? Part D Your dream of becoming rich has just come true. You have won the State of Tranquility’s Lottery. The State offers you two payment plans for the $5 million jackpot. You can take annual payments of $250,000 for the next 20 years or $2,867,480 today. a. If your investment rate over the next 20 years is 8%, which payoff will you choose? b. If your investment rate over the next 20 years is 5%, which payoff will you choose? c. At what investment rate will the annuity stream of $250,000 be the same as the lump sum payment of $2,867,480? BU340V Chapter 4.pptx Financial Management: Core Concepts Fourth Edition Chapter 4 The Time Value of Money (Part 2) Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. If this PowerPoint presentation contains mathematical equations, you may need to check that your computer has the following installed: 1) MathType Plugin 2) Math Player (free versions available) 3) NVDA Reader (free versions available) 1 Learning Objectives (1 of 2) 4.1Compute the future value of multiple cash flows. 4.2Determine the future value of an annuity. 4.3Determine the present value of an annuity. 4.4Adjust the annuity equation for present value and future value for an annuity due and understand the concept of a perpetuity. 4.5Distinguish between the different types of loan repayments: discount loans, interest-only loans, and amortized loans. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. Learning Objectives (2 of 2) 4.6Build and analyze amortization schedules. 4.7Calculate waiting time and interest rates for an annuity. 4.8Apply the time value of money concepts to evaluate the lottery cash flow choice. 4.9Summarize the 10 essential points about the time value of money. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 4.1 Future Value of Multiple Payment Streams (1 of 2) With unequal periodic cash flows, treat each of the cash flows as a lump sum and calculate its future value over the relevant number of periods. Sum up the individual future values to get the future value of the multiple payment streams. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. Figure 4.1 The Time Line of a Nest Egg Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 4.1 Future Value of Multiple Payment Streams (2 of 2) Example 1: Future Value of an Uneven Cash Flow Stream Jim deposits $3,000 today into an account that pays 10% per year, and follows it up with three more deposits at the end of each of the next 3 years. Each subsequent deposit is $2,000 higher than the previous one. How much money will Jim have accumulated in his account by the end of 3 years? Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 4.1 Future Value of Multiple Payment Streams (Example 1 Answer) (1 of 2) FV = PV × (1 + r)n FV of cash flow at T0 = $3,000 × (1.10)3 = $3,000 × 1.331= $3,993.00 FV of cash flow at T1 = $5,000 × (1.10)2 = $5,000 × 1.210= $6,050.00 FV of cash flow at T2 = $7,000 × (1.10)1 = $7,000 × 1.100= $7,700.00 FV of cash flow at T3 = $9,000 × (1.10)0 = $9,000 × 1.000= $9,000.00 Total = $26,743.00 Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 4.1 Future Value of Multiple Payment Streams (Example 1 Answer) (2 of 2) Alternative method: Using the cash flow (CF) key of the calculator, enter the respective cash flows. CF0 = −$3000; CF1 = −$5000; CF2 = −$7000; CF3 = −$9000; Next calculate the NPV using I = 10%; NPV = $20,092.41; Finally, using PV = −$20,092.41; n = 3; I = 10%; PMT = 0; CPT FV = $26,743.00 Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 4.2 Future Value of an Annuity Stream (1 of 5) Annuities are equal, periodic outflows/inflows, e.g. rent, lease, mortgage, car loan, and retirement annuity payments. An annuity stream can begin at the start of each period (annuity due) as is true of rent and insurance payments or at the end of each period, (ordinary annuity) as in the case of mortgage and loan payments. The formula for calculating the future value of an annuity stream is as follows: where PMT is the term used for the equal periodic cash flow, r is the rate of interest, and n is the number of periods involved. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 4.2 Future Value of an Annuity Stream (2 of 5) Example 2: Future Value of an Ordinary Annuity Stream Jill has been faithfully depositing $2,000 at the end of each year since the past 10 years into an account that pays 8% per year. How much money will she have accumulated in the account? Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 4.2 Future Value of an Annuity Stream (3 of 5) Example 2: Answer Future Value of Payment One= $2,000 × 1.089 = $3,998.01 Future Value of Payment Two= $2,000 × 1.088 = $3,701.86 Future Value of Payment Three= $2,000 × 1.087 = $3,427.65 Future Value of Payment Four= $2,000 × 1.086 = $3,173.75 Future Value of Payment Five= $2,000 × 1.085 = $2,938.66 Future Value of Payment Six= $2,000 × 1.084 = $2,720.98 Future Value of Payment Seven= $2,000 × 1.083 = $2,519.42 Future Value of Payment Eight = $2,000 × 1.082 = $2,332.80 Future Value of Payment Nine= $2,000 × 1.081 = $2,160.00 Future Value of Payment Ten= $2,000 × 1.080 = $2,000.00 Total Value of Account at the end of 10 years$28,973.13 Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 4.2 Future Value of an Annuity Stream (4 of 5) Example 2: Answer Formula method where, PMT = $2,000; r = 8%; and n = 10 FVIFA → [((1.08)10 − 1) ÷ 0.08] = 14.486562, FV = $2000 × 14.486562 → $28,973.13 Using a financial calculator N = 10; PMT = −2,000; I = 8; PV = 0; CPT FV = 28,973.13 Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 4.2 Future Value of an Annuity Stream (5 of 5) Using an excel spreadsheet Enter = FV(8%,10, −2000, 0, 0); Output = $28,973.13 Rate, Nper, Pmt, PV, Type Type is 0 for ordinary annuities and 1 for annuities due Using FVIFA table (A-3) Find the FVIFA in the 8% column and the 10 period row; FVIFA = 14.486 FV = 2000 × 14.4865 = $28.973.13 Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. Figure 4.3 Interest and Principal Growth with Different Interest Rates for $100-Annual Payments Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 4.3 Present Value of an Annuity (1 of 5) To calculate the value of a series of equal periodic cash flows at the current point in time, we can use the following simplified formula: The last portion of the equation, is the present value interest factor of an annuity (PVIFA). Practical applications include figuring out the nest egg needed prior to retirement or lump sum needed for college expenses. Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. Figure 4.4 The Time Line of a Present Value of an Annuity Stream Copyright © 2019, 2016, 2013 Pearson Education, Inc. All Rights Reserved. 4.3 Present Value of an Annuity (2 of 5) Example 3: Present Value of an Annuity John wants to make sure that he has saved up enough money prior to the year in which his daughter begins college. Based on current estimates, he figures that college expenses will amount to $40,000 per year for 4 years (ignoring any inflation or tuition increases during the 4 years of college). How much money will John need to have accumulated in an account that earns 7% per year, just prior to the